Mathematical modeling of an inclined solar water distillation system

An inclined solar water distillation (ISWD) system, which generates distilled water (i.e., condensate) and hot water at the same time, was modeled and simulated. In the parametric studies, the effects of feed water mass flow rate and solar intensity on the system parameters were investigated. Finally, the system was simulated using actual deviations of solar intensity and environment temperature during a typical summer day in North Cyprus. The system can generate 3.5–5.4 kg (per m² absorber plate area) distilled water during a day (i.e., 7 am till 7 pm). The temperature of the produced hot water reached as high as 60°C, and the average water temperature was about 40°C, which is good enough for domestic use, depending on the type of feed water. The simulation results are in good agreement with the experimental results.     

Etude numérique de l'évaporation dans un courant d'air humide laminaire et turbulent d'un film d'eau ruisselant sur une plaque inclinée

The authors have proposed an appropriate model based on the liquid film transfer equations which are one‐dimensional, partially two‐dimensional and two‐dimensional. They have compared their results with those of other works and studied the influence of the liquid mass flow rate and the inclined angle. They have shown that the interracial heat transfer is dominated by the latent heat transfer; the contribution of the sensible heat is only important in the turbulent region where the interfacial temperature and the evaporating mass flux are practically constant and the thickness of the liquid film is uniform. For the adiabatic plate, the liquid mass flow rate and the inclined angle have no influence on the transfers. For the isothermal or the heated plate, the liquid mass flow rate essentially influences the turbulent region by reducing the interrfacial temperature and the heat and mass transfer coefficients. However, the inclination angle affects mainly the laminar region by increasing the interfacial velocity, reducing the film thickness and has little effects on the transfer coefficients.     

Simultaneous film evaporation and condensation on a two-directionally inclined surface

A theoretical analysis of the effects of inclination on the heat transfer rate during the simultaneous film evaporation on one side and film condensation on the other side of a solid flat plate is presented.The decrease of the evaporating film thickness due to the two-dimensional nature of the flow is relatively small. Hence, the corresponding increase in the overall transfer coefficient is practically insignificant.For a system in which the evaporating film is sustained by a vertically down-flowing liquid, the main effect of the inclination of the plane from the horizontal is due to the formation of an unwetted area. Some practical conclusions related to a bundle of conduits are suggested.In view of the conclusions, the extension of the flat plane analysis by sectional integration to inclined conduits is not warranted.     

The Use of the VOF‐Model to Study the Wetting of Solid Surfaces

The laminar liquid rivulet flow on an inclined flat metal plate and wavy metal plate is taken as a test case to validate the CFD‐simulation results using the VOF (Volume of Fluid) multiphase flow model. The local rivulet thickness was measured using an optically assisted mechanical sensor and compared with the simulation results. The circular shape of the rivulet profile has been proven for an inclined plate. Glycerin water mixtures with different concentrations were used in the experiments. Two theoretical models to describe this laminar rivulet flow in comparison to the experimental and CFD results are discussed.     

波纹壁面上流动液膜涡的生成特性

针对液膜在非平整壁面上流动过程中生成涡的现象,基于VOF方法,采用FLUENT软件模拟了三维波纹壁面上的液膜流动。研究了波纹结构内涡结构的演化过程,分析入口Reynolds数、波纹结构、壁面倾角、流体黏度和表面张力对波纹结构内涡结构的影响。结果表明：随着时间的演化,涡的大小和形状不断变化,最终达到稳定。且涡结构变化对自由液面的波动影响显著。较低Re和波形度时,波纹结构内不易形成涡,随着Re和波形度增大,产生涡且涡呈增大趋势,涡的形态也随之改变,自由液面位置升高,其相位滞后于波纹壁面。当壁面倾角改变时,波纹结构内的涡特性变化较大,液膜厚度略有增加,而自由液面相位不明显。表面张力对涡结构有显著影响,液膜流动过程中不容忽视。流体黏性改变时,波纹结构内涡的大小和形状无明显的变化。黏度变小和忽略表面张力时,液膜厚度均变薄。以上结果为工业设备生产、运行和设计提供了一定参考依据。     

斜板沉降器处理负荷的计算

依据双膜模型和液滴在斜板层膜上的有效聚结 ,对层膜层流的临界雷诺数进行了关联 ,得出了斜板沉降器处理负荷的计算式。经实验数据验证 ,处理负荷的计算误差在 8%以内。     

NUMERICAL ANALYSIS OF HYDROMAGNETIC GRAVITY-DRIVEN THIN FILM MICROPOLAR FLOW ALONG AN INCLINED PLANE

The steady, gravity-driven, incompressible, hydromagnetic, laminar flow of a viscous, electrically conducting, micropolar liquid along an inclined plane subjected to a uniform transverse magnetic field is examined, neglecting surface tension effects. The governing two-dimensional boundary layer equations in an (x, y) coordinate in the absence of pressure gradient are reduced to a pair of ordinary differential equations for linear momentum and angular momentum conservation subject to generalized micro-rotation and velocity boundary conditions at the plane surface. The film thickness is assumed uniform along the plane. The reduced conservation equations are then nondimensionalized and solved numerically with the network simulation method (NSM) and Sparrow-Quack-Boerner local non-similarity method (LNM) for a wide range of the governing dimensionless fluid dynamics parameters. Excellent agreement is obtained between the NSM and LNM solutions. The computations indicate that increasing micropolarity, i.e., Eringen number, elevates micro-rotation magnitudes but reduces linear velocity, i.e., decelerates the flow. The study has significant applications in magnetic field control of materials processing systems.     

A solar desalination system using humidification–dehumidification process: experimental study and comparison with the theoretical results

In this study, influence of the different system operating conditions on the performance of a solar desalination system using humidification-dehumidification process have been investigated experimentally under the climatological conditions of Ankara (40°N, 33°E), Turkey. An experimental set-up that consists of a double-pass flat plate solar air heater with two glass covers, pad humidifier, dehumidifying exchanger and water storage tank was designed and manufactured. Working principle of the set-up is based on the idea of closed water and open-air cycles. A series of tests were performed on it in outdoor environment, in order to assess the effect of mass flow rate of the feed water, process air and cooling water, double-pass flat plate solar air heater, initial water temperature and amount of the water inside the storage tank on the productivity of the system. Additionally, an evacuated tubular solar water heater unit was integrated to the existing system and the effect of this integration on the performance of the system was examined. Solar radiation, wind speed, relative humidity, mass flow rate of the feed water, process air and cooling water, mass of condensate water and temperatures at various locations were obtained during the experiments.

The results of the experimental study showed that under certain operating conditions, the system productivity decreases about 15% if double-pass solar air heater is not used and significant improvement on the productivity of the system is achieved by increasing the initial water temperature inside the storage tank. In addition, productivity of the system increases with increasing the feed water mass flow rate and quantity of water inside the storage tank. However, productivity of the system remains approximately the same when the air mass flow rate is increased. Moreover, increasing the cooling water mass flow rate results in the improvement on the productivity of the system investigated. Finally, results obtained from the present investigation were compared with the theoretical study and a good agreement between them is observed.     

Coating flows with interfacial air drag. A nonlinear theory

The problem of the coating flow of a Newtonian liquid under the influence of a contiguous air flow is considered. The effect of the air flow is simulated by a constant tangential viscous shearing, calculated as the average skin friction per unit area of a boundary layer air flow over a smooth flat plate. Predictions are obtained for the liquid flow characteristics in cases of cocurrent and countercurrent forced air flows. Significant changes in the liquid film thickness start to occur when the absolute value of a dimensionless shearing number, Tn, exceeds 0.01. This value is not sensitive to the other flow parameters. The study is limited to low and moderate liquid Reynolds numbers, when the surface tension forces have considerable to noticeable effect.     

EXPERIMENTAL STUDY OF GRAVITY-DRIVEN FILM FLOW OF NON-NEWTONIAN FLUIDS

In this research the problem of a thin layer of a power law liquid falling down an inclined plate was studied experimentally. Three different carboxymethyl cellulose (CMC) solution concentrations (1.1%, 1.5%, and 2%), which are extensively used in industry, have been selected as the operating fluid, and their rheology, surface tension, and contact angle have been determined. Dynamics of the falling film has been studied by image acquisition techniques, and by using image processing methods the velocity of falling film, film thickness, and the shape of the falling film have been investigated. The inclined plate with different inclination angles φ (0 < φ < π/2), and nonidentical surfaces (ceramic, aluminum, and glass) were used to study the effect of inclination, rheological properties, and contact angle on the vital parameters mentioned earlier. These variables are embedded in dimensionless groups, Weber (We), Reynolds (Re), and Froude (Fr) numbers, and some correlations were devised to relate dimensionless velocity distribution parameters and film thickness to these dimensionless groups.     

Etude numérique de l'influence de l'inclinaison sur l'évaporation d'un film liquide s'écoulant sur une paroi plane isotherme ou à flux de chaleur imposé

The authors study numerically, by using an implicit centred difference method with non-uniform grid, the effects of inclination on the evaporation of liquid film flowing on a horizontal or inclined isotherm flat plate with the assumption of existing two-dimensional laminar boundary-layers with variable physical properties. In the case of an humid air-water system, they compare their results with those of other authors and study the influence of the entrance air velocity and the inclined angle of plate. They show that for an isotherm plate, the inclined angle effects heat and mass transfer, especially for low flow air velocity and for an inclined angle less than 10°. In this domain, the interfacial temperature is so high as the inclined angle increases which causes an increase of the density of flux of vapor, of the latent heat of vaporization and a reduction of draining length. For the heated plate, it is always for an inclined angle than 10°, that the effects of this parameter and air velocity are very important on the film thickness and its interfacial velocity. Opposite to the case of an isotherm plate, air velocity increase causes a reduction of interfacial temperature; inclined angle has less effect on temperature, density of latent heat of vaporisation and on heat and mass transfer at the interface. Generally, for an isotherm or heated plate, heat transfer is dominated by liquid-vapor phase transition.     

Laboratory test of solar distillator with a heat penetrating plate having a bend

A new idea was tested for a solar distillator with wick attached behind an inclined heat penetrating plate.The plate is bended at the center line and a tube is penetrated below the crease of bending. Liquid is fed to the tube and is flooded from two holes near the inlet and then forms a meniscus between the outer surface of the tube and the wick. This meniscus extends along the tube and part of the flow is deliver to the wick. This liquid feeding system is capable of preventing scale formation by forming film flow over the wick surface.The size of the experimental apparatus was 450 mm long and 160 mm wide for one side of the plate. The plate was attached with fibrous sheet as the wick. The idea was tested by using water without heating and satisfactorily uniform film flow was confirmed over all surface of the plate in a feed range between 0.5 and 4.75 kg/h·m.The design procedure was also provided on the basis of process simulation at practical conditions.     

Liquid layer characteristics in gas-liquid flow in slightly inclined pipes: Effect of non-ionic surfactant additives

The influence of non-ionic surfactant additives on the interfacial structure during both co-current gas-liquid upflow and downflow in slightly inclined pipes is investigated. Experiments are conducted in a 24 mm i.d. pipe for various gas-liquid flow rates and pipe inclination angles (β=±1° and ±3° from the horizontal position). Dilute aqueous solutions of the non-ionic surfactant Triton X-100 are employed, in order to study the effect of the additive on the flow pattern and the liquid layer characteristics (i.e. mean layer thickness, amplitude and frequency of the interfacial waves). In particular, the new data of the liquid layer characteristics indicate how the interfacial structure and the transition between the various flow regimes, during co-current gas-liquid flow in slightly inclined pipes, are affected by the addition of small amounts of the non-ionic surfactant.     

斜板沉降器内油粒运动规律分析

在对斜板间连续流场的研究基础上,采用离散相模型结合自编程对在错流、并流和逆流的3种流动形式中Stokes油滴运动规律进行模拟计算:该油滴在垂直于板方向上浮速度相同,与流动形式无关,其上浮时间正比于分离场的高度,在板间距相同条件下,上浮到上板所需时间相同,但逆流时油滴迁移距离最短,与流动形式有关;油滴运动位移和浮升时间随斜板倾角α增大而增长。     

Stability analysis of heated thin liquid-film flows with constant thermal boundary conditions

To answer the questions on the behavior of liquid flows under complicatedly combined actions of stresses, evaporation and temperature-dependent surface tension effects, thin liquid layers flowing under gravity down an inclined plane uniformly heated from below are considered There may be two thermal boundary conditions on the hot plate, i e , either constant heat flux or fixed temperature By using long-wave approximation, the nonlinear evolution equations governing the two-dimensional surface waves have been derived upto O(ε²) and O(ε) for the constant heat flux and the fixed temperature case, respectively Here the small parameter ε(l) is the ratio of the characteristic length scale parallel to the flow to the initial basic film thickness The linear and the nonlinear stability analyses are also performed by using numerical calculations Consequently, the flow subjected to the constant heat flux can be marked as a more stable system than the flow mechanism at a fixed-tem-perature boundary condition.     

Prediction of effective area and liquid hold-up in structured packings by CFD

Interfacial effective area and liquid hold-up in structured packing geometries are investigated using the volume of fluid method. Three-dimensional numerical simulations of gas–liquid flow on inclined plane plate and in a structured packing are performed. The VOF method is used to capture the gas–liquid interface motion. After a first validation case on the wetting phenomena prediction on an inclined plane plate, the effective interfacial area, the liquid hold-up and the degree of wetting of packing are studied as function of liquid flow rate and wall surface characteristic (adherence contact angle). Results show that the liquid flow-rate and the contact angle play a significant role. It is found that the interfacial effective area and the degree of wetting of packing increase as the liquid flow rate increases and as the contact angle decreases. Moreover, under the influence of the contact angle, different liquid film shapes are observed. The simulations results are compared to experimental data available in literature. This work shows that the CFD is a powerful tool to investigate performance characteristics of structured packings. Moreover, this work shows how CFD can be used as an effective tool to provide information on fluid flow behavior and determination of interfacial area, liquid hold-up and minimum flow-rate to ensure complete wetting. These parameters could be further used in process simulation at larger scale for the development and the design of efficient packings.     

斜板式气液分离器的设计

针时常规卧式和立式气液分离器的缺点和不足,论述了斜板式气液分离器的分离机理和结构特点,提出了采用斜板结构有利于提高气液分离效率的新思路,建立了斜板式气液分离器的理论计算公式,并以常规卧式分离器和立式分离器为例进行了对比计算。结果表明斜板式气液分离器可以提高气液分离器的分离效率,即在相同结构外径与处理量的前提下,可以缩短分离器的长度。或在相同结构条件下可以降低带出液体的粒径。     

Experimental study of liquid distribution in a column with a structured packing

Reflective fiber optic sensors are used to measure the thickness of a liquid film on geometrically complex surfaces inside a distillation column with a structured packing and countercurrent flow of gas and liquid. Distributions of the liquid-film thickness as a function of flow-rate parameters for an elementary region (cell) of a geometrically repeated pattern in a structured packing consisted of Koch 1Y corrugated plates and for the column cross section are presented. It is shown that the flow conditions characterized by the detachment of liquid films from the plate by air flow (until the complete column “flooding”) is accompanied by a sharp increase in the pressure drop in the column. Inside the cell, the liquid forms menisci in the zone of plate contact points. The countercurrent air flow reduces the fluctuations of the film thickness by 1.5 to 2 times on the edge and side downslopes of the corrugation.     

Instabilities induced by an electrostatic field over the film flow down an inclined plane

A study of the instabilities in the interaction of an electrostatic field with a thin liquid film flowing under gravity down an inclined plane is presented. First, the long-wave stability conditions are studied by perturbing the evolution equation of film height about its steady-state solution. Three limits of flow systems are considered, i.e., static state, Reynolds number Re = 0(1) and Re = 0(1/ξ). Here ξ(≪1) is the ratio of the characteristic length scale parallel to the flow to the primary film thickness. Next, the long-wave behavior of the thin film flow is examined with the electrostatic potential of a Gaussian function in the two limits of Reynolds number, i.e., Re = 0(1) and Re =0(l/≪). These results are also compared with those from a full-scale explicit calculation. Finally, wave-growth rates are calculated from the Orr-Sommerfeld equation to show the stability to wave number with and without the electric field. The effect of the electric field is to lessen the range of the wave number in which the thin film flow remains stable.